My friends and I were having a heated debate yesterday. The question was whether when one squats is the downward force exerted on the legs (hips to feet) the same if the shoulders and arms help support the bar OR if the arms are just there to hold the bar in place? The arms holding the bar do not move they are just flexed and holding the bar off the shoulders. The distance the bar has to go down is equal to the distance the legs are going down in both problems.

If there are any variables that i could have forgotten to say please add them, thanks!

If you support the bar with your arms, then that weight is necessarily applied through your shoulders. Your shoulders are probably higher up your back than the bar would normally be, which means that the force exerted by your legs/hips has to be greater.

That said, I think the primary issues with supporting the bar with your arms are that it is easy to hurt your wrists/elbows this way and that it is more difficult to keep the bar stationary. (Ideally, you want the bar to only move vertically during your squat, but if you support it with your arms it is easier for the bar to drift forward/back.)

Edit: It is worth checking out the book Starting Strength by Mark Rippetoe if you’re interested in the mechanics behind lifting.

Your muscles aren't static machines with constant output. For example, people doing pull ups often cheat by swinging their legs. This lowers the weight being lifted by the arms. Something similar could happen in your scenario.